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A30.2 A current i flows through an inductor L in the direction from point b toward point a. There is zero resistance in the wires of the inductor. If the current is decreasing, A. the potential is greater at point a than at point b. B. the potential is less at point a than at point b. C. The answer depends on the magnitude of di/dt compared to the magnitude of i. D. The answer depends on the value of the inductance L. E. both C. and D. are correct. © 2012 Pearson Education, Inc. Chapter 31 { © 2012 Pearson Education, Inc. Alternating Current Circuits Phasors and alternating currents The left diagram shows the voltage across an AC source as a function of time On the right is a simple phasor diagram. © 2012 Pearson Education, Inc. D’Arsonval galvanometer • • A d’Arsonval galvanometer measures the current through it (see Figures 26.13 and 26.14 below). Many analog electrical instruments, such as ammeters and voltmeters, use a galvanometer in their design. © 2012 Pearson Education, Inc. Root-mean-square values To measure alternating current you need something more complicated than a simple analog voltmeter – e.g., a circuit like the one to the right. © 2012 Pearson Education, Inc. Resistor in an ac circuit • • Ohm’s Law gives the voltage amplitude across a resistor: VR = IR. Figure 31.7 shows the circuit, the current and voltage as functions of time, and a phasor. © 2012 Pearson Education, Inc. Inductor in an ac circuit • • The voltage amplitude across the inductor is VL = IXL. The voltage leads the current by 90◦ © 2012 Pearson Education, Inc. Capacitance in an ac circuit • • The voltage amplitude across the capacitor is VC = IXC The voltage follows the current by 90◦ © 2012 Pearson Education, Inc. Comparing ac circuit elements • • Table 31.1 summarizes the characteristics of a resistor, an inductor, and a capacitor in an ac circuit. Figure 31.11 (below) shows graphs of resistance and reactance. © 2012 Pearson Education, Inc. A useful application: the loudspeaker • The woofer (low tones) and the tweeter (high tones) are connected in parallel across the amplifier output. (See Figure 31.12 shown here.) © 2012 Pearson Education, Inc. Q31.1 A resistor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the resistor and the instantaneous voltage vab across the resistor? A. i is maximum at the same time as vab. B. i is maximum one-quarter cycle before vab. C. i is maximum one-quarter cycle after vab. D. not enough information given to decide © 2012 Pearson Education, Inc. A31.1 A resistor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the resistor and the instantaneous voltage vab across the resistor? A. i is maximum at the same time as vab. B. i is maximum one-quarter cycle before vab. C. i is maximum one-quarter cycle after vab. D. not enough information given to decide © 2012 Pearson Education, Inc. Q31.2 An inductor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the inductor and the instantaneous voltage vab across the inductor? A. i is maximum at the same time as vab. B. i is maximum one-quarter cycle before vab. C. i is maximum one-quarter cycle after vab. D. not enough information given to decide © 2012 Pearson Education, Inc. A31.2 An inductor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the inductor and the instantaneous voltage vab across the inductor? A. i is maximum at the same time as vab. B. i is maximum one-quarter cycle before vab. C. i is maximum one-quarter cycle after vab. D. not enough information given to decide © 2012 Pearson Education, Inc. Q31.3 A capacitor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the capacitor and the instantaneous voltage vab across the capacitor? A. i is maximum at the same time as vab. B. i is maximum one-quarter cycle before vab. C. i is maximum one-quarter cycle after vab. D. not enough information given to decide © 2012 Pearson Education, Inc. A31.3 A capacitor is connected across an ac source as shown. For this circuit, what is the relationship between the instantaneous current i through the capacitor and the instantaneous voltage vab across the capacitor? A. i is maximum at the same time as vab. B. i is maximum one-quarter cycle before vab. C. i is maximum one-quarter cycle after vab. D. not enough information given to decide © 2012 Pearson Education, Inc.